People with virtually no technical knowledge of computers are right to be cautious about building a custom computer. There are many sensitive parts in a system that can be damaged by someone who isn't careful. Take, for example, the thermal paste on the base of the HSF. Sure, with the intel stock HSF it's preapplied and you can easily just put it in place and push down the pins for easy assembly, however if, for example, one of the pins didn't go down properly and you had to take it off to try again, chances are that preapplied thermal paste will be ruined and you'll never get the thin, consistent (i.e. without bubbles) application between the HSF and CPU that it needs to conduct heat properly.
That said, if the person is careful and guided well (most people turn to noobtoob for this), it can be as simple as building a bookcase. Take care with the heavy parts, make sure all the screws (or, in computers, wires and plugs) are in the right place, and it'll all go smoothly.
In response to exangel, several others, and to reiterate my own point, I can't speak for most PB or Acer laptops - just the 2 I have. I never heard about the bad press for PB and never bothered checking, but I do know that I've not seen any PB laptops in store since shortly after I bought this one 4 years ago. As for Acer, they seem to be competing in popularity with HP and Sony (Samsung and Toshiba just don't seem that popular in shops these days). Of the 3, Acer are generally cheapest, HP gaudiest (although with the most extras) and Sony the most expensive (although they give a 'premium' quality to their lines, which I personally never liked the look of). Until reading about it on this forum, I've also never heard complaints over Acer laptops (which apparantly randomly stop working), so I can't say anything bad about them until I witness it myself. HP, on the other hand, have a running trend of design flaws and overheating problems in several of their laptops (making them a very hit-and-miss laptop manufacturer), including the HP Pavillion tx2550ea that both me and my brother have.
My PB laptop has a 2.2Ghz T7500 (upgraded from a 1.5Ghz Centrino Duo) and a GeForce 8600M powering it. The 8600M is infamous for dying in most laptops, yet mine has never let me down. What I do know, however, is that they didn't use any thermal paste on the CPU. I don't know if that's standard practice in PB or other laptop manufacturers, but putting my own Zalman thermal paste on the new CPU brought down the average temperature by 7-10C. Otherwise, sometimes it gets a lil hot (nothing a notebook cooling pad doesn't fix), but it works great.
My dad's Acer Aspire 5740 has a Core i5-430M and Intel GMA 4500HD. It's brilliant for chess, has a decent battery life, doesn't get very hot at all, and can even play games like Borderlands and Left 4 Dead at low settings at playable speeds. Also the case is a smooth, curvy, shiny blue, and I like blue. The only problem with it is that I can't update the Intel display drivers without losing the display, which sucks, but can't be helped. It is also the first laptop I own (technically, it's still my dad's) that can achieve full WiFi-N speed with my router (my HP tablet laptop can't).
I've also spent a lot of time over the last couple years watching the Acer line, especially their higher end laptops. The Aspire 8742 looks awesome with its media controls (even my dad likes it, although he'll never go for a laptop so expensive) and it can come with Core i7 and a HD5850 at its most expensive configuration. That's pretty much as powerful as a mid-ranged PC. Unfortunately I can't afford it, so I've only been able to look and dream of it in the local Micro Anvika store.
Back to the main point, which laptop the OP should buy, I always recommend to read the reviews of both first. If they both have good reviews, and similar specs, then go for the one you think looks best (after all, you'll probably be showing it off to your friends shortly after getting it).